Question

Find the volume of a pyramid with a square base, where the side length of the base is
7, point, 2, cm
7.2 cm and the height of the pyramid is
10, point, 4, cm
10.4 cm. Round your answer to the nearest tenth of a cubic centimeter.

Answer 1

To find the volume of a pyramid, you can use the formula:

\[
V = \frac{1}{3} \times B \times h
\]

where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height of the pyramid.

In this case, the base is a square, so the area \( B \) can be calculated as:

\[
B = \text{side length}^2
\]

Given that the side length of the base is \( 7.2 \, \text{cm} \):

\[
B = (7.2 \, \text{cm})^2 = 51.84 \, \text{cm}^2
\]

The height \( h \) of the pyramid is given as \( 10.4 \, \text{cm} \).

Now, plug these values into the volume formula:

\[
V = \frac{1}{3} \times 51.84 \, \text{cm}^2 \times 10.4 \, \text{cm}
\]

Calculating the volume step-by-step:

1. First, multiply the area of the base by the height:

\[
51.84 \, \text{cm}^2 \times 10.4 \, \text{cm} = 539.136 \, \text{cm}^3
\]

2. Then, divide by 3 to find the volume:

\[
V = \frac{539.136 \, \text{cm}^3}{3} = 179.712 \, \text{cm}^3
\]

Rounding this to the nearest tenth:

\[
V \approx 179.7 \, \text{cm}^3
\]

Thus, the volume of the pyramid is approximately **179.7 cubic centimeters**.